A216217 Smallest k such that 6^n - 2*k*3^n - 1 and 6^n - 2*k*3^n + 1 are twin primes or 0 if no solution, n > 1.

1, 2, 3, 0, 3, 11, 33, 9, 26, 6, 34, 138, 51, 19, 33, 246, 66, 31, 167, 73, 13, 716, 138, 148, 138, 339, 447, 41, 131, 41, 9, 178, 778, 337, 543, 2154, 213, 1216, 454, 183, 678, 442, 157, 381, 297, 1476, 54, 1201, 1942, 1566, 572, 3708, 3261, 3672, 1087, 306

Offset

2,2

Comments

Conjecture: there is only one zero term: a(5) = 0.

The PFGW script computes 2*a(n).

Links

Pierre CAMI, Table of n, a(n) for n = 2..400

Example

6^2 - 2*1*3^2 - 1 = 17, 17 and 19 twin primes so a(2)=1.
6^3 - 2*2*3^3 - 1 = 107, 107 and 109 twin primes so a(3)=2.
6^4 - 2*3*3^4 - 1 = 809, 809 and 811 twin primes so a(4)=3.
6^5 - 2*k*3^5 - 1 and 6^5 - 2*k*3^5 + 1 for k=1 to 30 have no twin prime solution so a(5)=0.

Mathematica

Table[k = 0; While[k++; p = 6^n - 2*k*3^n - 1; p > 0 && ! (PrimeQ[p] && PrimeQ[p + 2])]; If[p <= 0, 0, k], {n, 2, 50}] (* T. D. Noe, Mar 15 2013 *)

Prog

(PFGW & Scriptify)
PFGW64 -lout.txt -f in.txt
in.txt file :
SCRIPT
DIM k
DIM n, 1
DIMS t
LABEL loop1
SET n, n+1
IF n>400 THEN END
SET k, 0
LABEL loop2
SET k, k+2
SETS t, %d, %d\,; n; k
PRP 6^n-k*3^n-1, t
IF ISPRP THEN GOTO a
GOTO loop2
LABEL a
SETS t, %d, %d\,; n; k
PRP 6^n-k*3^n+1, t
IF ISPRP THEN GOTO loop1
GOTO loop2

Crossrefs

Cf. A205322 (similar, but powers of 2).

Sequence in context: A180188 A316607 A194365 * A253283 A261719 A137663

Adjacent sequences: A216214 A216215 A216216 * A216218 A216219 A216220

Keyword

nonn

Author

Pierre CAMI, Mar 13 2013

Status

approved